The connections created by the ADO Connection Editor for managed code are not automatically brought over with you application but they can be exported on the development computer and then imported on the COBOL Server machine.
Open up the ADO Connection Editor on the development computer and click the Export tab. Here you can select the connections that you wish to export to an xml file.
Bring this file to your Server computer and start ADO Connection editor on it under Start menu > All Programs > COBOL Server 2.0 > Data Tools and then use the import tab to import the connection from the XML file.
The ADO Data Provider does have to be installed and setup in order for this to be successful.